As Arthur Riordan's musical, Improbable Frequency, returns to Dublin, novelist Anne Enright ponders his distinctive talent.

Sometimes I find myself thinking about the inside of Arthur Riordan's brain. I wander around a little, rooting about in the corners, upsetting piles of old Penguin paperbacks, a rack of Nicole Fahri jackets, a complete set of Butler's Lives of the Saints; I look at the vinyl spilling out of its sleeves, and wonder what is on the records, Yeats reading, "I will arise and go now" in that silly high voice he had, or one of the very many bands that I have never heard of but that Arthur Riordan has, or nothing - a more interesting silence.

Riordan makes the phrase "a well-stocked mind" sound like a branch of Habitat - this brain is furnished in the high-baroque Irish tradition of Joyce and Myles na gCopaleen, it has the range of popular reference of Pat McCabe. This brain possesses many folds and infolds. It is not somewhere you can get out of easily. Its most recent creation is Improbable Frequency, a musical starring Myles himself, the physicist Erwin Schrödinger and the English poet John Betjeman, all of whom were, coincidentally, in Dublin during the Emergency. As the chorus of British diplomats sing:

Is it smugness or insurgency,

That makes them say 'Emergency'?

I feel it lacks the urgency

Of 'World War Two'

This, from that instant classic, Be Careful Not to Patronise the Irish (though they don't object to patronising you).

Improbable Frequency is a satire on Irish national grandiosity, whipped along by a Mylesian farrago of a plot. It is also a thriller and a romance, with some great Broadway belters that are half-ironic and pure delight. And it rhymes. All of it. Every single line of it rhymes, and puns, and does a little somersault, just for show. The whole damn thing is probably a palindrome. As one set of lovers (and code-breaking spies) sing about the first time they met:

At the crossword solvers' lunch

In the Savoy, in London town

You were the one across from me -

So I was not too down.

The Rough Magic production, which moves to the Abbey tomorrow, swept the board at the recent Irish Times/ESB theatre awards, and this added to the sense that something had come into its own. Could it be that Arthur Riordan's peculiar genius was turning into pure genius in front of our eyes; that we had a handle now on this slippery writer, with his delight in tricks, clues, puns, his ability to move between parody and homage, his particular, highly political world view?

The question you must ask of a talent this distinctive is, "Where did it come from?" to which the answer can only partly be "Fermoy". Even to his friends, he remains something of an enigma. Arthur Riordan is so quietly subversive and so self-deprecating that it is difficult not to refer to him by his first name; still, the time has come to afford him that honour, allowed to male tennis players and writers, of becoming his surname. It is what his work deserves.

Riordan's first play - and not a lot of people remember this - was produced in Player's Theatre in TCD (where I was also a student at the time). It was written in rhyming couplets, and it told the story of the early martyr and actor St Philemon. Since then, Riordan's shift into the mainstream has been steady, if slow. It began in 1983 when a marathon reading of Shakespeare's plays produced The Merchant of Ennis, in which Riordan played Shylock in the character of Eamonn de Valera.

Waking up in a cold theatre at dawn, I remember walking across the cobbles of Front Square to the sound of, "My daughter, my ducats", and the sight of Arthur with his sloping nose and greatcoat - Dev to the life. There was something about the maddened parsimony of the Merchant that suited Dev perfectly - also the way he kept ordering people around all the time, and would not be thwarted.

Riordan has always played Dev with steely rage, an immovability, that turns the viewers into increasingly giddy children. By the time the sun was fully up, the rest of the cast was weak with the pure subversion of it. Dev however, was not weak. Dev, though defeated, remained unbowed.

I had a strong sense of the uncanny when I first saw "Dev" and it hasn't really left me. A few years later I directed a series of sketches called We Found de Valera in Our Fridge for the late-night TV show Nighthawks. In them, Riordan's Dev arrives to live in the apartment of Diarmuid and Gráinne, a middle-class couple played with deadpan glee by Gina Moxley and Mark O'Regan. The sketches were a compound of good jokes and bad puns, based on what might be called a clash of aspirations. Dev eats all Gráinne's contraceptive pills, for example, after she tells him that they "give her independence".

Riordan loves genre. What was distinctive about his scripts for TV was that they were so perfectly pitched as a mini-sitcom. Not a word of the dialogue was changed by director or actors, and this ability to draft and redraft was equally evident in the more substantial and satirical work "Dev" did with the stage shows The Emergency Sessions (key number Céad Míle Fáilte Bitch) and Rap Éire (hit tune: There's a Bit of Fianna Fáil in Us All). He has also written The Last Temptation of Michael Flatley for the Macra na Feirme drama groups, in which the characters speak in the rhythm of an Irish jig.

In person, Riordan is very likeable. He is also private and sometimes slightly abstracted, in the manner of someone who has more amusing problems to solve, on the inside of his head. At its most baleful, this talent is like Beckett's Molloy figuring out the right way to suck the 16 pebbles that are distributed between his coat and trouser pockets (Beckett is also a strong influence on Riordan's work).

His delight in the cryptic means that his scripts, although always playful, are never produced quickly, and by the time the material arrives on the page it is often richly complex. Still, like a lot of people who store up good jokes, Riordan's first impulse is to entertain, and his parallel career as an actor and founding member of Rough Magic has sharpened his sense of the audience.

He may know high culture, but he does not produce it: he may not even believe in it - though who is to say? I suspect he does believe in Eamonn de Valera, for example: that the conservative, the dark and the patriarchal aspects of Irish culture produce a hectic response in him that is the source of much of the hilarity we see on stage.

When I first met Arthur, I was very impressed by his shirt, which was a super-trendy top with a cartoon-strip design. This might sound quite ordinary now, as shirts go, but it was as remarkable in 1983 as was a verse play about the martyrdom of the actor-saint Philemon.

Riordan seemed like someone who had spent time in America, but he had not spent time in America. He had spent time in Fermoy. Or more correctly, he had spent time reading everything and watching everything while growing up in Fermoy. And this slightly dandified small-town sensibility is key to his satiric tone.

There is a part of him that is always 17, hanging around; a part that is thrilled by the smallness of the Irish, cute about cute-hoorism, and skittish about authority of all kinds. Added to this is an extensive knowledge of Irish history - underneath and through the gags, Riordan is saying something completely serious about how we got to where we think we are.

The most quoted line he ever wrote came from We Found de Valera in Our Fridge, when Gráinne asks "Dev" if he would like a drink.

"Yes, a Michael Collins please."

"Don't you mean a Tom Collins?"

"No, a Michael Collins. Two shots and then you hit the road."

Boom boom. Of course it was outrageous. Later, after Nighthawks was taken off the air and I was doing a lot of weekend overtime deep in the mines of children's TV, I sometimes wondered was it this joke, or another, or all of them put together, that stopped my climb up the dungheap that was RTÉ in those days. "Dev" stillthrew a long shadow - I should have seen it when I walked across those cobblestones at dawn - but I never had the slightest tinge of regret: working with Arthur Riordan always felt like a small triumph, to me.

The character of "Dev" does not appear in Improbable Frequency. When he took off the big overcoat, the writer in Riordan finally separated from the performer, and was given free rein. The resulting explosion of scale and perspective gave us the first ever musical about Irish neutrality, quantum mechanics, and the connection between the two.

What Riordan will do next is anyone's guess. It is in there somewhere, lurking like Schrödinger's cat in a corner of his remarkable brain.